Write down the gradient of the line L₁.

A second line L₂ is perpendicular to L₁.

Write down the gradient of L₂.

The point (5, 3) is on L₂.

Determine the equation of L₂.

Lines L₁ and L₂ intersect at point P.

Using your graphic display calculator or otherwise, find the coordinates of P.

\(\frac{-2}{{5}}\)     (A1)     (C1)

\(\frac{5}{{2}}\)     (A1)(ft)     (C1)

Note: Follow through from their answer to part (a).

\(3 = \frac{5}{2} \times 5 + c\)     (M1)

Notes: Award (M1) for correct substitution of their gradient into equation of line. Follow through from their answer to part (b).

\(y = \frac{5}{2}x - \frac{19}{2}\)     (A1)(ft)

OR

\(y - 3 = \frac{5}{2}(x - 5)\)     (M1)(A1)(ft)     (C2)

Notes: Award (M1) for correct substitution of their gradient into equation of line. Follow through from their answer to part (b).

(3, −2)     (A1)(ft)(A1)(ft)     (C2)

Notes: If parentheses not seen award at most (A0)(A1)(ft). Accept x = 3, y = −2. Follow through from their answer to part (c), even if no working is seen. Award (M1)(A1)(ft) for a sensible attempt to solve \(2x + 5y = −4\) and their \(y = \frac{5}{2}x - \frac{19}{2}\) or equivalent, simultaneously.